A note on the component structure in random intersection graphs with tunable clustering

We study the component structure in random intersection graphs with tunable clustering, and show that the average degree works as a threshold for a phase transition for the size of the largest component. That is, if the expected degree is less than one, the size of the largest component is a.a.s. of logarithmic order, but if the average degree is greater than one, a.a.s. a single large component of linear order emerges, and the size of the second largest component is at most of logarithmic order.Comment: 8 pages, Published at http://www.combinatorics.org/Volume_15/PDF/v15i1n10.pdf by the Electronic Journal of Combinatorics (http://www.combinatorics.org

Normaltillriktning av typsnittet Resultat : Jämförelse av två metoders resultat

Typsnitt tillverkade för både skärm och tryck är allt vanligare och speciellt webbläsare ställer tekniska krav på typsnitten. De flesta webbläsare förstår sig inte på fontens kerning information utan slopar det och litar på normaltillriktningen. I mitt arbete undersöker jag hurudan inverkan de två sätten att göra normaltillriktningen, för hand eller med auto-spacing funktionen, har på typsnittets färg. Som utgångspunkt använder jag mig av två versioner av typsnittet “Resultat” som jag sedan jämför med varandra. Resultat är ett sans-serif typsnitt som jag själv skapat. Målet med arbetet är att ge klarhet om vilkendera metoden producerar en jämnare färg, att utforska typiska drag i normaltillriktningen som orsakas av auto-spacing samt att förstå vilka för- och nackdelar båda metoderna har. Eftersom arbetet inte är en teoretisk studie baserar den sig på den erfarenhet jag fått från att skapa mitt egna typsnitt. Normaltillriktningen baserar sig på redan existerande metoder som presenteras i arbetet. I undersökningen kom det fram att normaltillriktning för hand producerar en jämnare färg. Auto-spacing gav ett hyfsat resultat men kantmarginalerna för bokstäver med oregelbundna former visade sig vara konstiga vilket ledde till en ojämn färg. Att göra normaltillriktningen för hand gav ett bättre resultat men tog avsevärt längre jämfört med auto-spacing. Avslutningsvis reflekterar jag kring hela processen och hur jag kan använda denna kunskap i framtida typsnitt.Typefaces designed for both screen and print are becoming more common and especially web browsers add technical limitations to the typefaces. Most web browser doesn’t understand the kerning information in a font and defaults to the letter-spacing. In my thesis I’ll focus on how the two ways of doing the letter-spacing, by hand or by using the autospacing function, affect the color of the typeface. As a starting point I’ve used two versions of the typeface “Resultat” which I compare against each other. Resultat is a sansserif typeface that I’ve made myself. The goal with this thesis is to show which method produces a more even color, examine typical characteristics in letter-spacing caused by auto-spacing and to understand what pros and cons each method has. This isn’t a theoretical study and will be based on the experience I got from designing my own typeface. The letter-spacing will be based on already existing methods which will be presented in the thesis. During the research I discovered that letter-spacing by hand produces a much more even color. Auto-spacing gave an ok result, although the sidebearings of letters with irregular shapes had some issues resulting in an uneven color. Letter-spacing by hand produced a much better result but took a considerable amount of time compared to autospacing. Finally I reflect on the whole process and think about how I will use this knowledge in future typefaces

A dynamic network in a dynamic population: asymptotic properties

We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model we derive criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming the node population grows to infinity. We also obtain an explicit expression for the degree correlation $\rho$ (of neighbouring nodes) which shows that $\rho$ is always positive irrespective of parameter values in one of the two treated submodels, and may be either positive or negative in the other model, depending on the parameters

A Discussion of Discrimination and Fairness in Insurance Pricing

Indirect discrimination is an issue of major concern in algorithmic models. This is particularly the case in insurance pricing where protected policyholder characteristics are not allowed to be used for insurance pricing. Simply disregarding protected policyholder information is not an appropriate solution because this still allows for the possibility of inferring the protected characteristics from the non-protected ones. This leads to so-called proxy or indirect discrimination. Though proxy discrimination is qualitatively different from the group fairness concepts in machine learning, these group fairness concepts are proposed to 'smooth out' the impact of protected characteristics in the calculation of insurance prices. The purpose of this note is to share some thoughts about group fairness concepts in the light of insurance pricing and to discuss their implications. We present a statistical model that is free of proxy discrimination, thus, unproblematic from an insurance pricing point of view. However, we find that the canonical price in this statistical model does not satisfy any of the three most popular group fairness axioms. This seems puzzling and we welcome feedback on our example and on the usefulness of these group fairness axioms for non-discriminatory insurance pricing.Comment: 14 page